## C++ Program to Implement Network_Flow Problem Full Project For Beginners

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• Post category:c++

`main.cpp`

``````/*
* C++ Program to Implement Network Flow Problem
*/
#include <iostream>
#include <climits>
#include <cstring>
#include <queue>
#define V 6
using namespace std;

/*
*  Returns true if there is a path from source 's' to sink 't' in
* residual graph. Also fills parent[] to store the path *
*/
bool bfs(int rGraph[V][V], int s, int t, int parent[])
{
bool visited[V];
memset(visited, 0, sizeof(visited));
queue <int> q;
q.push(s);
visited[s] = true;
parent[s] = -1;
while (!q.empty())
{
int u = q.front();
q.pop();

for (int v=0; v<V; v++)
{
if (visited[v]==false && rGraph[u][v] > 0)
{
q.push(v);
parent[v] = u;
visited[v] = true;
}
}
}
return (visited[t] == true);
}

/*
*  Returns tne maximum flow from s to t in the given graph
*/
int fordFulkerson(int graph[V][V], int s, int t)
{
int u, v;
int rGraph[V][V];
for (u = 0; u < V; u++)
{
for (v = 0; v < V; v++)
rGraph[u][v] = graph[u][v];
}
int parent[V];
int max_flow = 0;

while (bfs(rGraph, s, t, parent))
{
int path_flow = INT_MAX;
for (v=t; v!=s; v=parent[v])
{
u = parent[v];
path_flow = min(path_flow, rGraph[u][v]);
}
for (v = t; v != s; v = parent[v])
{
u = parent[v];
rGraph[u][v] -= path_flow;
rGraph[v][u] += path_flow;
}
max_flow += path_flow;
}
return max_flow;
}
/*
* Main Contains Menu
*/
int main()
{
int graph[V][V] = { {0, 16, 13, 0, 0, 0},
{0, 0, 10, 12, 0, 0},
{0, 4, 0, 0, 14, 0},
{0, 0, 9, 0, 0, 20},
{0, 0, 0, 7, 0, 4},
{0, 0, 0, 0, 0, 0}
};

cout << "The maximum possible flow is " << fordFulkerson(graph, 0, 5);

return 0;
}``````